A pet door apparatus (10) discloses a pet door frame (12), an opening (34), and closure flap (36) which is rotatable for at least partly closing the opening or extending away from the opening. A magnet (102) and magnetically attractable element are respectively on one or the other of the flap and frame, and an actuator can move the magnet or magnetically attractable element to change the distance, and magnetic attraction force, between them. A blocking member (176) attached to a side part (28) of the frame is movable under gravitational force and due to engaging cam surfaces (196, 198), from an extended, raised position for partially closing a gap (160) between the flap and frame, to a retracted, lowered position, and back to the raised, extended position by magnetic attraction between a magnet (164) on the flap and another magnet (190) on the frame.